Relativistic spin precession in the double pulsar.

Abstract

The double pulsar PSR J0737-3039A/B consists of two neutron stars in a highly relativistic orbit that displays a roughly 30-second eclipse when pulsar A passes behind pulsar B. Describing this eclipse of pulsar A as due to absorption occurring in the magnetosphere of pulsar B, we successfully used a simple geometric model to characterize the observed changing eclipse morphology and to measure the relativistic precession of pulsar B's spin axis around the total orbital angular momentum. This provides a test of general relativity and alternative theories of gravity in the strong-field regime. Our measured relativistic spin precession rate of 4.77 degrees (-0 degrees .65)(+0 degrees .66) per year (68% confidence level) is consistent with that predicted by general relativity within an uncertainty of 13%.

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arXiv:0807.2644v1 [astro-ph] 16 Jul 2008
Relativistic Spin Precession in the Double Pulsar
Rene P. Breton,1∗Victoria M. Kaspi,1Michael Kramer,2
Maura A. McLaughlin,3,4Maxim Lyutikov,5Scott M. Ransom,6
Ingrid H. Stairs,7Robert D. Ferdman,7,8
Fernando Camilo9, Andrea Possenti10
1Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada
2Jodrell Bank Observatory, University of Manchester, Manchester, M13 9PL, UK
3Department of Physics, West Virginia University, Morgantown, WV 26506, USA
4National Radio Astronomy Observatory, Green Bank, WV 24944, USA
5Department of Physics, Purdue University, West Lafayette, IN 47907, USA
6National Radio Astronomy Observatory, Charlottesville, VA 22903, USA
7Department of Physics and Astronomy, University of British Columbia,
Vancouver, BC V6T 1Z1, Canada
8LPCE / CNRS, F-45071 Orleans cedex 2, France
9Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA
10INAF - Osservatorio Astronomico di Cagliari, Poggio dei Pini, 09012 Capoterra, Italy
∗To whom correspondence should be addressed; E-mail: bretonr@physics.mcgill.ca.
The double pulsar PSR J0737−3039A/B consists of two neutron stars in a
highly relativistic orbit that displays a roughly 30-second eclipse when pulsar
A passes behind pulsar B. Describing this eclipse of pulsar A as due to absorp-
tion occurring in the magnetosphere of pulsar B, we successfully use a simple
geometric model to characterize the observed changing eclipse morphology
and to measure the relativistic precession of pulsar B’s spin axis around the
total orbital angular momentum. This provides a test of general relativity
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and alternative theories of gravity in the strong-field regime. Our measured
relativistic spin precession rate of 4.77+0.66
−0.65
◦yr−1(68% confidence level) is con-
sistent with that predicted by general relativity within an uncertainty of 13%.
Spin is a fundamental property of most astrophysical bodies, making the study of its grav-
itational interaction an important challenge (1). Spin interaction manifests itself in different
forms. For instance, we expect the spin of a compact rotating body in a binary system with
another compact companion to couple gravitationally with the orbital angular momentum (rel-
ativistic spin-orbit coupling) and also with the spin of this companion (relativistic spin-spin
coupling) (2,3). Observing such phenomena provides important tests for theories of gravity,
because every successful theory must be able to describe the couplings and to predict their
observational consequences. In a binary system consisting of compact objects such neutron
stars, one can generally consider the spin-orbit contribution acting on each body to dominate
greatly the spin-spin contribution. This interaction results in a precession of the bodies’ spin
axis around the orbital angular momentum of the system, behavior we refer to as relativistic
spin precession.
While relativistic spin precession is well studied theoretically in general relativity (GR),
the same is not true of alternative theories of gravity and hence, quantitative predictions of
deviations from GR spin precession do not yet exist (2). For instance, it is expected that in
alternative theories relativistic spin precession may also depends on strong self-gravitational
effects, i.e. the actual precession may depend on the structure of a gravitating body (2). In the
weak gravitational fields encountered in the solar system, these strong-field effects generally
cannot be detected (5,6,7). Measurements in the strong-field regime near massive and compact
bodies such as neutron stars and black holes are required. Relativistic spin precession has been
observed in some binary pulsars [e.g. (8,9,10)], but it has usually only provided a qualitative
confirmation of the effect. Recently, the binary pulsar PSR B1534+12 has allowed the first
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quantitative measurement of this effect in a strong field, and although the spin precession rate
was measured to low precision, it was consistent with the predictions of GR (11).
Here we report a precision measurement of relativistic spin precession using eclipses ob-
served in the double pulsar (12,13). This measurement, combined with observational access to
both pulsarorbits in thissystem, allowsus to constrain quantitativelyrelativisticspin precession
in the strong-field regime within a general class of gravitational theories that includes GR.
PSR J0737−3039A/B consists of two neutron stars, both visible as radio pulsars, in a rela-
tivistic 2.45-hour orbit (12,13). High-precision timing of the pulsars, having spin periods of 23
ms and 2.8 s (hereafter called pulsars A and B, respectively), has already proven to be the most
stringent test-bed for GR in the strong-field regime (14), and enables four independent timing
tests of gravity, more than any other binary system.
The orbital inclination of the double pulsar system is such that we observe the system al-
most perfectly edge-on. This coincidence causes pulsar A to be eclipsed by pulsar B at pulsar
A’s superior conjunction (13). The modestly frequency-dependent eclipse duration, about 30
s, corresponds to a region extending ∼1.5×107m (15). The light curve of pulsar A during its
eclipse shows flux modulations that are spaced by half or integer numbers of pulsar B’s rota-
tional period (16). This indicates that the material responsible for the eclipse corotates with
pulsar B. The relative orbital motions of the two pulsars and the rotation of pulsar B thus allow
a probe of different regions of pulsar B’s magnetosphere in a plane containing the line of sight
and the orbital motion.
Synchrotron resonance with relativistic electrons is the most likely mechanism for efficient
absorption of radio emission over a wide range of frequencies. In the model proposed by Lyu-
tikov and Thompson (1), this absorbing plasma corotates with pulsar B and is confined within
the closed field lines of a magnetic dipole truncated by the relativistic wind of pulsar A. The
dipole magnetic moment vector makes an angle α with respect to the spin axis of pulsar B,
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whose orientation in space can be described by two angles: the colatitude of the spin axis with
respect to the total angular momentum of the system, θ, and the longitude of the spin axis, φ
(see Fig. 1 for an illustration of the system geometry). Additional parameters characterizing the
plasma opacity, µ, the truncation radius of the magnetosphere, Rmag, and the relative position
of pulsar A with respect to the projected magnetosphere of pulsar B, z0, are also included in the
model (1).
We monitored the double pulsar from December 2003 to November 2007 using the Green
Bank Telescope in West Virginia; most of the data were acquired as part of the timing observa-
tions reported in (14). The data used for our analysis were taken at 820MHz with the SPIGOT
instrument (18), which provides 1024 frequency channels across a 50MHz bandwidth. Data
for a total of 63 eclipses of pulsar A were collected over the 4-year period, with many ob-
tained during semi-annual concentrated observing campaigns. We dedispersed each eclipse
data set by adding time shifts to frequency channels in order to compensate for the frequency-
dependent travel time of radio waves in the ionized interstellar medium and we then folded
them at the predicted spin period of pulsar A using the pulsar analysis packages PRESTO (19)
and SIGPROC (20) (see (14) for details about the radio timing). Next, we extracted the rela-
tive pulsed flux density of pulsar A by fitting each folded interval for the amplitude of a high
signal-to-noise ratio pulse profile template made from the integrated pulse observed during the
several-hour observation that includes each eclipse. Finally, we normalized the flux densities so
the average level outside the eclipse region corresponded to unity. We chose the time resolution
of our eclipse light curves to equal, on average, four individual pulses of pulsar A (∼91ms).
In addition to the flux density, we determined the orbital phase and the spin phase of pulsar
B corresponding to each data point of our time series. Orbital phases were derived from the
ephemeris published in (14). Spin phases were empirically measured from data folded at the
predicted period of pulsar B in a way similarto that described abovefor pulsar A. Over the four-
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year monitoring campaign, we found significant changes in pulsar B’s pulse profile, likely due
to the precession of its spin axis, which were also reported in (21). Around 2003, the average
pulse profile was unimodal, resembling a Gaussian function. It evolved such that by 2007, it
displayed two narrow peaks. Using the pulse peak maximum as a fiducial reference point is
certainly not appropriate. We find, however, that the unimodal profile gradually became wider
and then started to form a gap near the center of its peak. Since then, the outer edges of the
pulse profile have not significantly changed but the gap evolved such that two peaks are now
visible. This lets us presume that the underlying average profile is reminiscent of a Gaussian-
like profile to which some “absorption” feature has been superimposed near the center, leaving
a narrow peak on each side. We therefore defined the fiducial reference point to lie at the center
of the unimodal “envelope” that we reconstructed from the first ten Fourier bins of the pulse
profile, which contains 512 bins in total (see Fig. S2 of the Supporting Online Material for an
illustration of the pulse profile evolution).
We implemented the eclipse modeling of our data in two steps: the fitting of individual
eclipse profiles and the search for evolution of the geometry of pulsar B. We first searched the
full phase space to identify best-fit values of six parameters (see Supporting Online Material for
more details). Then, we reduced thenumber offree parameters to thesubset (θ, φ, α) describing
the orientation of pulsar B’s spin and magnetic axes by fixing the other parameters to their best-
fit values: µ = 2, Rmag = 1.29◦(projected value in terms of orbital phase) and z0/Rmag =
−0.543 (see Fig. 1). Finally, we performed a high-resolution mapping of the likelihood of
this subspace in order to investigate subtle changes in the geometry. Lyutikov and Thompson
(1) predicted that such changes, due to relativistic spin precession, could affect the eclipse
light curve. In principle, relativistic spin precession of pulsar B’s spin axis around the total
angular momentum should induce a secular change of the longitude of the spin axis, φ, while
the magnetic inclination, α, and the colatitude of the spin axis, θ, are expected to remain fixed
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